Instructions
Teach one of your Pokemon Surf and Whirlpool so you can enter the correct part of the Whirl Islands. Teach Flash to another Pokemon to illuminate the cave once you are inside.
Walk or fly to Olivine City, then head to Route 40 to the east. Surf down Route 40 to Route 41.
Surf south along Route 41 until you reach the northeasternmost of the Whirl Islands, and use Whirlpool to get through the rocks surrounding the island. Surf around until you reach the cave entrance.
Use Flash to illuminate the cave.
Head up and to the right, and jump off the first ledge. There will be a branch in the path. Continue alone the uppermost path and jump over the next ledge. Continue as far to the right as you can, then head up.
Go down the ladder.
Head down, then turn left. Keep going left until you reach a branch in the path, and head down. You should see another ladder if you've gone the right way.
Climb down the next ladder.
Head straight down, then take a slight turn to the right before heading down again.
Talk to the man blocking the path. After a brief conversation, he will let you pass.
Follow the ramp downward. There are no branches in the path so just continue until you reach the bottom.
Enter the cave. Lugia will appear after a short scene with the Kimono Girls. Save your game before challenging the legendary Pokemon.